To really increase the realism of the metaphor, in the future when such content is stolen, they should refuse to serve it to library users. They could explain that, regrettably, the journal issue I seek is currently missing due to a recent theft, and assure me that they are working as fast as possible to recover the stolen documents.
Physical books impose a natural limit on the number of simultaneous checkouts. If a book is very popular, the library will buy more copies to accommodate demand. If a PDF is popular, the publisher expects the library to buy more copies.
It's artificial scarcity, but this is hardly new. The number of books in a library was never limited by the cost of paper.